Preprint Article Version 1 This version is not peer-reviewed

Renormalization and Fractals among Sets beyond (Empty) Boundaries

Version 1 : Received: 4 November 2019 / Approved: 6 November 2019 / Online: 6 November 2019 (06:47:34 CET)

How to cite: Adachi, S. Renormalization and Fractals among Sets beyond (Empty) Boundaries. Preprints 2019, 2019110055 (doi: 10.20944/preprints201911.0055.v1). Adachi, S. Renormalization and Fractals among Sets beyond (Empty) Boundaries. Preprints 2019, 2019110055 (doi: 10.20944/preprints201911.0055.v1).

Abstract

In previous studies, the authors utilized a single-dimensional operationalization of species density that implies induction of hierarchy and time with certain topologies. For further clarification of induced fractals including the relation to renormalization in physics, here a theoretical development is proposed based on a newly identified fact, namely that scaling parameters for magnetization exactly correspond to imaginary parts of Riemann zeta nontrivial zeros. An analogy to magnetization and accompanying Fake Monster Algebra is invoked to lend support to this theory, along with empirical species density data for a wild Dictyostelia community. A master torus and a Lagrangian/Hamiltonian are derived expressing fractal structures as a solution for diminishing divergent terms in renormalization.

Subject Areas

topology; fractal; renormalization; species

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